Lommel Differential Equation

A generalization of the Bessel Differential Equation (Watson 1966, p. 345),

$$z^2 {d^2y\over dz^2}+z{dy\over dz}-(z^2+\nu^2)y = kz^{\mu+1}.$$

A further generalization gives

$$z^2 {d^2y\over dz^2}+z{dy\over dz}-(z^2+\nu^2)y = \pm kz^{\mu+1}.$$

The solutions are Lommel Functions.

See also Lommel Function

References

Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.